3 research outputs found
Existence theory by front-tracking for general nonlinear hyperbolic systems
ABSTRACT. We consider the Cauchy problem for a strictly hyperbolic, NxN quasilinear system in one-space dimension
(1) u_t+A(u) u_x=0,,
u(0,x) = overline u (x),,
where u=u(t,x)=(u_1(t,x),dots, u_N(t,x)), u ---> A(u) is a smooth matrix-valued map, and the initial data overline u is assumed to have small total variation.
We present a front tracking algorithm that generates piecewise
constant approximate solutions converging in L^1_{loc} to the
vanishing viscosity solution of (1), which, by the results of Bianchini and Bressan, is the unique limit of solutions to the (artificial) viscous parabolic approximation
u_t+A(u) u_x=mu, u_{xx}, u(0,x) = bar u (x),,
as mu--> 0. In the conservative case where A(u) is the Jacobian matrix of some flux function F(u) with values in R^N, the limit of front tracking approximations provides a weak solution of the system of conservation laws u_t+F(u)_x=0, satisfying the Liu admissibility conditions.
These results are achieved under the only assumption of strict hyperbolicity of the matrices A(u), uin R^N. In particular, our construction applies to general strictly hyperbolic system of conservation laws with characteristic fields that do not satisfy the standard conditions of genuine non linearity or of linear degeneracy in the sense of Lax, or in the generalized sense of Liu
How Technologies Can Enhance Open Policy Making and Citizen-Responsive Urban Planning: MiraMap - A Governing Tool for the Mirafiori Sud District in Turin (Italy)
This paper explores an innovative approach to open policymaking and citizen-responsive urban plan-ning. It reports on project MiraMap carried out by the Politecnico di Torino (the Polytechnic University of Turin). The project engages both citizens and the Public Administration in a reporting process con-cerning critical issues, as well as positive trends and resources within the Mirafiori Sud administrative area of Turin (Italy), through the use of a digital collaborative platform. The experiment was a real case study geared at evaluating the use of open source technologies to foster e-participation in urban plan-ning. MiraMap has been set up with an eye to achieving integration within the current administrative management process and to involving new actors in the decision-making process through a “collective governance” approach. Therefore, this paper seeks to set up a methodological (and technological) framework, which is seen as crucial for addressing the complexity and dynamics of urban planning and programming, by integrating the perspectives of citizens through their actual engagemen
Digital Platforms for Enhancing Participatory Design and Urban Regeneration: A Case Study in Turin (Italy)
This chapter explores an innovative approach to open policy-making and citizen-responsive urban planning. It reports on the ongoig project MiraMap carried out by the Politecnico di Torino from 2013. It started creating a crowdmap, engaging both citizens and the Public Administration in a reporting process concerning issues, and resources within the Mirafiori Sud administrative area of Turin (Italy), until it became a digital collaborative platform. It was a real case study geared at evaluating the use of open source technologies. MiraMap has been set up by integrating current administrative management process and involving new actors in the decision-making process through. Today the project is focusing mostly on encouraging forms of co-design and co-production, including gaming components. The chapter seeks to set up a methodological and technological framework, by addressing the complexity of urban planning and integrating the perspectives of citizens through their actual engagement
